The structure of affine buildings / Richard M. Weiss.

Format:

Book

Author/Creator:

Weiss, Richard M. (Richard Mark), 1946-

Series:

Annals of mathematics studies ; no. 168.

Annals of mathematics studies ; no. 168

Language:

English

Subjects (All):

Buildings (Group theory).

Moufang loops.

Automorphisms.

Affine algebraic groups.

Physical Description:

1 online resource (381 p.)

Edition:

Course Book

Place of Publication:

Princeton, N.J. : Princeton University Press, c2009.

Language Note:

English

Summary:

In The Structure of Affine Buildings, Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about automorphisms, completions, and residues of these buildings. It also includes tables correlating the results in the locally finite case with the results of Tits's classification of absolutely simple algebraic groups defined over a local field. A companion to Weiss's The Structure of Spherical Buildings, The Structure of Affine Buildings is organized around the classification of spherical buildings and their root data as it is carried out in Tits and Weiss's Moufang Polygons.

Contents:

Frontmatter

Contents

Preface

Chapter 1. Affine Coxeter Diagrams

Chapter 2. Root Systems

Chapter 3. Root Data with Valuation

Chapter 4. Sectors

Chapter 5. Faces

Chapter 6. Gems

Chapter 7. Affine Buildings

Chapter 8. The Building at Infinity

Chapter 9. Trees with Valuation

Chapter 10. Wall Trees

Chapter 11. Panel Trees

Chapter 12. Tree-Preserving Isomorphisms

Chapter 13. The Moufang Property at Infinity

Chapter 14. Existence

Chapter 15. Partial Valuations

Chapter 16. Bruhat-Tits Theory

Chapter 17. Completions

Chapter 18. Automorphisms and Residues

Chapter 19. Quadrangles of Quadratic Form Type

Chapter 20. Quadrangles of Indifferent Type

Chapter 21. Quadrangles of Type E6, E7 and E8

Chapter 22. Quadrangles of Type F4

Chapter 23. Quadrangles of Involutory Type

Chapter 24. Pseudo-Quadratic Quadrangles

Chapter 25. Hexagons

Chapter 26. Assorted Conclusions

Chapter 27. Summary of the Classification

Chapter 28. Locally Finite Bruhat-Tits Buildings

Chapter 29. Appendix A

Chapter 30. Appendix B

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786612458361

9781282458369

1282458361

9781400829057

1400829054

OCLC:

647843271